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A second genus of regular ternary forms
Published online by Cambridge University Press: 26 February 2010
Extract
In the paper [2] Hsia noted that the forms x2+xy+y2+9z2 and x2+3y2+3yz+3z2 constitute a genus and that both forms are regular; he asked whether there exist any other genera containing two or more regular forms. In this note it is proved that the forms
are regular. They constitute a genus with discriminant 27 (in the normalization used by Brandt and Intrau in [1]). It is noteworthy that Hsia's genus has the same discriminant.
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